The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu${}_{2}$(BO${}_{3}$)${}_{2}$. Here, the authors present numerical evidence of a gapless liquid phase discuss connection to deconfined critical point. new exists parameter regime where recent high-pressure heat capacity measurements on SrCu${}_{2}$(BO${}_{3}$)${}_{2}$ did not detect any low-temperature order, contrast antiferromagnetic plaquette-singlet...

In this paper, we study the dissipative measure-valued solution to magnetohydrodynamic equations of 3D compressible isentropic flows with adiabatic exponent γ > 1 and prove that a is same as standard smooth classical long latter exists, provided they emanate from initial data (weak–strong) uniqueness principle.

High-voltage direct current (HVDC) transmission is a crucial way to solve the reverse distribution of clean energy and loads. The line commutated converter-based HVDC (LCC-HVDC) has become vital structure for due its high technological maturity economic advantages. During DC fault LCC-HVDC, such as commutation failure, reactive power regulation AC grid always lags control process, causing overvoltage in sending grid, which brings off-grid risk wind generation based on electronic devices....

The local maximal inequality for the Schr\"{o}dinger operators of order $\a>1$ is shown to be bounded from $H^s(\R^2)$ $L^2$ any $s>\frac38$. This improves previous result Sj\"{o}lin on regularity solutions fractional equations. Our method inspired by Bourgain's argument in case $\a=2$. extension $\a=2$ general confronts three essential obstacles: lack Lee's reduction lemma, absence algebraic structure symbol and inapplicable Galilean transformation deduction main theorem. We get around...

The intricate interplay between frustration and spin chirality has the potential to give rise unprecedented phases in frustrated quantum magnets. We examine ground state phase diagram of spin-1/2 square lattice J1-J2-Jx model by employing critical level crossings fidelity susceptibility (FS) using exact diagonalization (ED) with full symmetries. Our analysis reveals evolution highly symmetric energy levels as a function J2 at fixed Jx. During magnetic non-magnetic transition, precise...

The global-in-time existence of weak solutions to the viscous quantum Magnetohydrodynamic equations in a three-dimensional torus with large data is proved. global shown by using Faedo-Galerkin method and compactness techniques.

In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution incompressible Navier‐Stokes equation rigorously proven for well prepared initial data. Furthermore, associated rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider the compressible quantum Navier-Stokes-Poisson equations with a linear density-dependent viscosity. By use of singular pressure close to vacuum, prove global-in-time existence weak solutions in three-dimensional torus for large data sense distribution.

This paper is concerned with the convergence of time-dependent and nonisentropic Euler–Maxwell equations to compressible Euler–Poisson in a torus via nonrelativistic limit. By using method formal asymptotic expansions, we analyze limit for periodic problems prepared initial data. It shown that small parameter problem has unique solutions existing finite time interval where corresponding have smooth solutions. Furthermore, rigorously justified.

A two-temperature semiconductor model was used to investigate the non-equilibrium thermal transport in Ge2Sb2Te5 thin films caused by an ultrashort laser pulse ranging from atto- nanoseconds. In model, photo-excited carriers were considered based on absorbing mechanism. As a general rule, shorter pulses led equilibration time between carrier and lattice systems. However, minimum reach equilibrium (about 80 ps) obtained for both attosecond femtosecond pulses, which mainly determined material...

In this paper, a class of refinable functions is given by smoothening pseudo-splines in order to get divergence free and curl wavelets. The regularity stability them are discussed. Based on that, the corresponding Riesz wavelets constructed.

This work concerns the semilinear wave equation in three space dimensions with a power-like nonlinearity which is greater than cubic, and not quintic (i.e. energy-critical). We prove that scale-invariant Sobolev norm of any non-scattering solution goes to infinity at maximal time existence. gives refinement on known results energy-subcritical energy-supercritical equation, unified proof. The proof relies channel energy method, as arXiv:1204.0031, weighted spaces were introduced...

It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are also discussed.

In this paper, we will discuss asymptotic limit of non-isentropic compressible Euler-Maxwell system arising from plasma physics. Formally, give some different systems according to the corresponding scalings. Furthermore, recent results about convergence Euler-Poisson equations be given via non-relativistic regime.